Physics of a Discrete Cosmology

The classical stochastic models of Rideout and Sorkin [1] give indications that cosmological models of discrete spacetime might help to resolve fundamental questions in cosmology [2]. The Rideout Sorkin (RS) models are, however, only classical and to model the physics of the Big Bang and any pre-Big Bang epoch will require a quantum theory of spacetime. This project will investigate possible quantum cosmological discrete models. The parameters which specify the RS models provide the transition probabilities for discrete spacetimes to grow; a quantum generalisation will instead have transition amplitudes. The aim of the project is to discover physically well-motivated transition amplitudes and investigate the universes that result and in particular discover whether the cosmologies exhibit the same kind of cyclic behavior that is manifested in the classical models. The project will also study models of matter propagating in discrete backgrounds to extract observable signatures of discrete spacetime. The discreteness will cause microscopic effects that build up over long distances and this can be modelled using a diffusion equation with additional drift terms.

[1] A classical sequential growth dynamics for causal sets, Rideout, D. P. and Sorkin, R. D., Phys. Rev D61 (1999) 024002.
[2] Indications of causal set cosmology, Rafael D. Sorkin, Int. J. Theor. Phys. 39 (2000) 1731-1736